Net theory and its applications :: flows in networks /
Electrical, communication, transportation, computer, and neural networks are special kinds of nets. Designing these networks demands sophisticated mathematical models for their analysis. This book is the first to present a unified, comprehensive, and up-to-date treatment of net theory. It brings tog...
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1. Verfasser: | |
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Format: | Elektronisch E-Book |
Sprache: | English |
Veröffentlicht: |
London :
Imperial College Press,
2003.
|
Schriftenreihe: | Series in electrical and computer engineering ;
vol. 1. |
Schlagworte: | |
Online-Zugang: | Volltext |
Zusammenfassung: | Electrical, communication, transportation, computer, and neural networks are special kinds of nets. Designing these networks demands sophisticated mathematical models for their analysis. This book is the first to present a unified, comprehensive, and up-to-date treatment of net theory. It brings together elements of abstract graph theory and circuit analysis to network problems. |
Beschreibung: | 1 online resource (x, 660 pages) : illustrations |
Bibliographie: | Includes bibliographical references and index. |
ISBN: | 9781848161290 1848161298 1281865907 9781281865908 9786611865900 661186590X |
Internformat
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245 | 1 | 0 | |a Net theory and its applications : |b flows in networks / |c Wai-Kai Chen. |
260 | |a London : |b Imperial College Press, |c 2003. | ||
300 | |a 1 online resource (x, 660 pages) : |b illustrations | ||
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490 | 1 | |a Series in electrical and computer engineering ; |v vol. 1 | |
504 | |a Includes bibliographical references and index. | ||
588 | 0 | |a Print version record. | |
505 | 0 | |a 1. Graphs and networks. 1.1. Basic definitions of abstract graphs. 1.2. Operations on graphs. 1.3. Nonseparable graphs and bipartite graphs. 1.4. Planar graphs. 1.5. Dual graphs. 1.6. 2-isomorphism. 1.7. Matrices associated with a graph. 1.8. Directed graphs. 1.9. The circuit matrix associated with a planar graph or directed graph. 1.10. Summary and suggested reading -- 2. The shortest directed path problem. 2.1. Shortest directed paths. 2.2. Shortest directed path algorithms. 2.3. Multiterminal shortest directed paths. 2.4. Enumeration of the shortest directed paths by decomposition. 2.5. Summary and suggested reading -- 3. Maximum flows in networks. 3.1. Flows. 3.2. s-t cuts. 3.3. Maximum flow. 3.4. Ford-Fulkerson algorithm. 3.5. Layered nets. 3.6. A blocking flow algorithm. 3.7. Variants of the Ford-Fulkerson algorithm. 3.8. Karzanov algorithm. 3.9. Flows in undirected and mixed nets. 3.10. Flows in node-and-arc capacitated nets. 3.11. Summary and suggested reading -- 4. Minimum trees and communication nets. 4.1. Forests, subtrees and trees. 4.2. Minimum and maximum trees. 4.3. Minimum and maximum tree algorithms. 4.4. Terminal capacity matrix. 4.5. Synthesis of a flow-equivalent tree. 4.6. Synthesis of optimum undirected communication nets. 4.7. Oriented communication nets. 4.8. Summary and suggested reading -- 5. Feasibility theorems and their applications. 5.1. A supply-demand theorem. 5.2. An extended supply-demand theorem. 5.3. Circulation theorem. 5.4. Feasible circulation algorithm. 5.5. Flows in nets with lower bounds on arcs. 5.6. Feasible flows in node-and-arc capacitated nets. 5.7. Summary and suggested reading -- 6. Applications of flow theorems to subgraph problems. 6.1. The subgraph problem of a directed graph. 6.2. Digraphic sequences. 6.3. The subgraph problem of a graph. 6.4. Graphical sequences. 6.5. The (p, s)-matrix. 6.6. Realization of the 1-matrix and the (1, 0)-matrix. 6.7. Minimal transformations. 6.8. Summary and suggested reading -- 7. Signal-flow graphs. 7.1. The signal-flow graph. 7.2. Topological evaluation of determinants. 7.3. Topological evaluation of cofactors. 7.4. Topological solutions of linear algebraic equations. 7.5. Equivalence and transformation. 7.6. The matrix inversion. 7.7. Signal-flow graph formulation of feedback amplifier theory. 7.8. Matrix signal-flow graph. 7.9. The multiple-loop feedback amplifier theory. 7.10. Summary and suggested reading -- 8. Other net applications. 8.1. Boolean matrices and switching nets. 8.2. Tellegen's theorem. 8.3. Generalized signal-flow graphs. 8.4. Permutations by spaghetti Amida. 8.5. The Amida graph. 8.6. Graph decomposition and hybrid analysis of electrical networks. 8.7. Summary and suggested reading. | |
520 | |a Electrical, communication, transportation, computer, and neural networks are special kinds of nets. Designing these networks demands sophisticated mathematical models for their analysis. This book is the first to present a unified, comprehensive, and up-to-date treatment of net theory. It brings together elements of abstract graph theory and circuit analysis to network problems. | ||
546 | |a English. | ||
650 | 0 | |a Machine theory. |0 http://id.loc.gov/authorities/subjects/sh85079341 | |
650 | 0 | |a Nets (Mathematics) |0 http://id.loc.gov/authorities/subjects/sh85091044 | |
650 | 0 | |a Flowgraphs. |0 http://id.loc.gov/authorities/subjects/sh85049350 | |
650 | 0 | |a System analysis. |0 http://id.loc.gov/authorities/subjects/sh85131733 | |
650 | 2 | |a Systems Analysis |0 https://id.nlm.nih.gov/mesh/D013597 | |
650 | 6 | |a Réseaux (Mathématiques) | |
650 | 6 | |a Graphes de fluence. | |
650 | 6 | |a Analyse de systèmes. | |
650 | 6 | |a Théorie des automates. | |
650 | 7 | |a systems analysis. |2 aat | |
650 | 7 | |a MATHEMATICS |x Infinity. |2 bisacsh | |
650 | 7 | |a MATHEMATICS |x Logic. |2 bisacsh | |
650 | 7 | |a System analysis |2 fast | |
650 | 7 | |a Nets (Mathematics) |2 fast | |
650 | 7 | |a Flowgraphs |2 fast | |
650 | 7 | |a Machine theory |2 fast | |
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author | Chen, Wai-Kai, 1936- |
author_GND | http://id.loc.gov/authorities/names/n50059490 |
author_facet | Chen, Wai-Kai, 1936- |
author_role | |
author_sort | Chen, Wai-Kai, 1936- |
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contents | 1. Graphs and networks. 1.1. Basic definitions of abstract graphs. 1.2. Operations on graphs. 1.3. Nonseparable graphs and bipartite graphs. 1.4. Planar graphs. 1.5. Dual graphs. 1.6. 2-isomorphism. 1.7. Matrices associated with a graph. 1.8. Directed graphs. 1.9. The circuit matrix associated with a planar graph or directed graph. 1.10. Summary and suggested reading -- 2. The shortest directed path problem. 2.1. Shortest directed paths. 2.2. Shortest directed path algorithms. 2.3. Multiterminal shortest directed paths. 2.4. Enumeration of the shortest directed paths by decomposition. 2.5. Summary and suggested reading -- 3. Maximum flows in networks. 3.1. Flows. 3.2. s-t cuts. 3.3. Maximum flow. 3.4. Ford-Fulkerson algorithm. 3.5. Layered nets. 3.6. A blocking flow algorithm. 3.7. Variants of the Ford-Fulkerson algorithm. 3.8. Karzanov algorithm. 3.9. Flows in undirected and mixed nets. 3.10. Flows in node-and-arc capacitated nets. 3.11. Summary and suggested reading -- 4. Minimum trees and communication nets. 4.1. Forests, subtrees and trees. 4.2. Minimum and maximum trees. 4.3. Minimum and maximum tree algorithms. 4.4. Terminal capacity matrix. 4.5. Synthesis of a flow-equivalent tree. 4.6. Synthesis of optimum undirected communication nets. 4.7. Oriented communication nets. 4.8. Summary and suggested reading -- 5. Feasibility theorems and their applications. 5.1. A supply-demand theorem. 5.2. An extended supply-demand theorem. 5.3. Circulation theorem. 5.4. Feasible circulation algorithm. 5.5. Flows in nets with lower bounds on arcs. 5.6. Feasible flows in node-and-arc capacitated nets. 5.7. Summary and suggested reading -- 6. Applications of flow theorems to subgraph problems. 6.1. The subgraph problem of a directed graph. 6.2. Digraphic sequences. 6.3. The subgraph problem of a graph. 6.4. Graphical sequences. 6.5. The (p, s)-matrix. 6.6. Realization of the 1-matrix and the (1, 0)-matrix. 6.7. Minimal transformations. 6.8. Summary and suggested reading -- 7. Signal-flow graphs. 7.1. The signal-flow graph. 7.2. Topological evaluation of determinants. 7.3. Topological evaluation of cofactors. 7.4. Topological solutions of linear algebraic equations. 7.5. Equivalence and transformation. 7.6. The matrix inversion. 7.7. Signal-flow graph formulation of feedback amplifier theory. 7.8. Matrix signal-flow graph. 7.9. The multiple-loop feedback amplifier theory. 7.10. Summary and suggested reading -- 8. Other net applications. 8.1. Boolean matrices and switching nets. 8.2. Tellegen's theorem. 8.3. Generalized signal-flow graphs. 8.4. Permutations by spaghetti Amida. 8.5. The Amida graph. 8.6. Graph decomposition and hybrid analysis of electrical networks. 8.7. Summary and suggested reading. |
ctrlnum | (OCoLC)261127898 |
dewey-full | 511.3 |
dewey-hundreds | 500 - Natural sciences and mathematics |
dewey-ones | 511 - General principles of mathematics |
dewey-raw | 511.3 |
dewey-search | 511.3 |
dewey-sort | 3511.3 |
dewey-tens | 510 - Mathematics |
discipline | Mathematik |
format | Electronic eBook |
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Graphs and networks. 1.1. Basic definitions of abstract graphs. 1.2. Operations on graphs. 1.3. Nonseparable graphs and bipartite graphs. 1.4. Planar graphs. 1.5. Dual graphs. 1.6. 2-isomorphism. 1.7. Matrices associated with a graph. 1.8. Directed graphs. 1.9. The circuit matrix associated with a planar graph or directed graph. 1.10. Summary and suggested reading -- 2. The shortest directed path problem. 2.1. Shortest directed paths. 2.2. Shortest directed path algorithms. 2.3. Multiterminal shortest directed paths. 2.4. Enumeration of the shortest directed paths by decomposition. 2.5. Summary and suggested reading -- 3. Maximum flows in networks. 3.1. Flows. 3.2. s-t cuts. 3.3. Maximum flow. 3.4. Ford-Fulkerson algorithm. 3.5. Layered nets. 3.6. A blocking flow algorithm. 3.7. Variants of the Ford-Fulkerson algorithm. 3.8. Karzanov algorithm. 3.9. Flows in undirected and mixed nets. 3.10. Flows in node-and-arc capacitated nets. 3.11. Summary and suggested reading -- 4. Minimum trees and communication nets. 4.1. Forests, subtrees and trees. 4.2. Minimum and maximum trees. 4.3. Minimum and maximum tree algorithms. 4.4. Terminal capacity matrix. 4.5. Synthesis of a flow-equivalent tree. 4.6. Synthesis of optimum undirected communication nets. 4.7. Oriented communication nets. 4.8. Summary and suggested reading -- 5. Feasibility theorems and their applications. 5.1. A supply-demand theorem. 5.2. An extended supply-demand theorem. 5.3. Circulation theorem. 5.4. Feasible circulation algorithm. 5.5. Flows in nets with lower bounds on arcs. 5.6. Feasible flows in node-and-arc capacitated nets. 5.7. Summary and suggested reading -- 6. Applications of flow theorems to subgraph problems. 6.1. The subgraph problem of a directed graph. 6.2. Digraphic sequences. 6.3. The subgraph problem of a graph. 6.4. Graphical sequences. 6.5. The (p, s)-matrix. 6.6. Realization of the 1-matrix and the (1, 0)-matrix. 6.7. Minimal transformations. 6.8. Summary and suggested reading -- 7. Signal-flow graphs. 7.1. The signal-flow graph. 7.2. Topological evaluation of determinants. 7.3. Topological evaluation of cofactors. 7.4. Topological solutions of linear algebraic equations. 7.5. Equivalence and transformation. 7.6. The matrix inversion. 7.7. Signal-flow graph formulation of feedback amplifier theory. 7.8. Matrix signal-flow graph. 7.9. The multiple-loop feedback amplifier theory. 7.10. Summary and suggested reading -- 8. Other net applications. 8.1. Boolean matrices and switching nets. 8.2. Tellegen's theorem. 8.3. Generalized signal-flow graphs. 8.4. Permutations by spaghetti Amida. 8.5. The Amida graph. 8.6. Graph decomposition and hybrid analysis of electrical networks. 8.7. Summary and suggested reading.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Electrical, communication, transportation, computer, and neural networks are special kinds of nets. Designing these networks demands sophisticated mathematical models for their analysis. This book is the first to present a unified, comprehensive, and up-to-date treatment of net theory. 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id | ZDB-4-EBA-ocn261127898 |
illustrated | Illustrated |
indexdate | 2024-11-27T13:16:32Z |
institution | BVB |
isbn | 9781848161290 1848161298 1281865907 9781281865908 9786611865900 661186590X |
language | English |
oclc_num | 261127898 |
open_access_boolean | |
owner | MAIN DE-863 DE-BY-FWS |
owner_facet | MAIN DE-863 DE-BY-FWS |
physical | 1 online resource (x, 660 pages) : illustrations |
psigel | ZDB-4-EBA |
publishDate | 2003 |
publishDateSearch | 2003 |
publishDateSort | 2003 |
publisher | Imperial College Press, |
record_format | marc |
series | Series in electrical and computer engineering ; |
series2 | Series in electrical and computer engineering ; |
spelling | Chen, Wai-Kai, 1936- https://id.oclc.org/worldcat/entity/E39PBJyCCHRrC93Wrwjfkyvj4q http://id.loc.gov/authorities/names/n50059490 Net theory and its applications : flows in networks / Wai-Kai Chen. London : Imperial College Press, 2003. 1 online resource (x, 660 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier Series in electrical and computer engineering ; vol. 1 Includes bibliographical references and index. Print version record. 1. Graphs and networks. 1.1. Basic definitions of abstract graphs. 1.2. Operations on graphs. 1.3. Nonseparable graphs and bipartite graphs. 1.4. Planar graphs. 1.5. Dual graphs. 1.6. 2-isomorphism. 1.7. Matrices associated with a graph. 1.8. Directed graphs. 1.9. The circuit matrix associated with a planar graph or directed graph. 1.10. Summary and suggested reading -- 2. The shortest directed path problem. 2.1. Shortest directed paths. 2.2. Shortest directed path algorithms. 2.3. Multiterminal shortest directed paths. 2.4. Enumeration of the shortest directed paths by decomposition. 2.5. Summary and suggested reading -- 3. Maximum flows in networks. 3.1. Flows. 3.2. s-t cuts. 3.3. Maximum flow. 3.4. Ford-Fulkerson algorithm. 3.5. Layered nets. 3.6. A blocking flow algorithm. 3.7. Variants of the Ford-Fulkerson algorithm. 3.8. Karzanov algorithm. 3.9. Flows in undirected and mixed nets. 3.10. Flows in node-and-arc capacitated nets. 3.11. Summary and suggested reading -- 4. Minimum trees and communication nets. 4.1. Forests, subtrees and trees. 4.2. Minimum and maximum trees. 4.3. Minimum and maximum tree algorithms. 4.4. Terminal capacity matrix. 4.5. Synthesis of a flow-equivalent tree. 4.6. Synthesis of optimum undirected communication nets. 4.7. Oriented communication nets. 4.8. Summary and suggested reading -- 5. Feasibility theorems and their applications. 5.1. A supply-demand theorem. 5.2. An extended supply-demand theorem. 5.3. Circulation theorem. 5.4. Feasible circulation algorithm. 5.5. Flows in nets with lower bounds on arcs. 5.6. Feasible flows in node-and-arc capacitated nets. 5.7. Summary and suggested reading -- 6. Applications of flow theorems to subgraph problems. 6.1. The subgraph problem of a directed graph. 6.2. Digraphic sequences. 6.3. The subgraph problem of a graph. 6.4. Graphical sequences. 6.5. The (p, s)-matrix. 6.6. Realization of the 1-matrix and the (1, 0)-matrix. 6.7. Minimal transformations. 6.8. Summary and suggested reading -- 7. Signal-flow graphs. 7.1. The signal-flow graph. 7.2. Topological evaluation of determinants. 7.3. Topological evaluation of cofactors. 7.4. Topological solutions of linear algebraic equations. 7.5. Equivalence and transformation. 7.6. The matrix inversion. 7.7. Signal-flow graph formulation of feedback amplifier theory. 7.8. Matrix signal-flow graph. 7.9. The multiple-loop feedback amplifier theory. 7.10. Summary and suggested reading -- 8. Other net applications. 8.1. Boolean matrices and switching nets. 8.2. Tellegen's theorem. 8.3. Generalized signal-flow graphs. 8.4. Permutations by spaghetti Amida. 8.5. The Amida graph. 8.6. Graph decomposition and hybrid analysis of electrical networks. 8.7. Summary and suggested reading. Electrical, communication, transportation, computer, and neural networks are special kinds of nets. Designing these networks demands sophisticated mathematical models for their analysis. This book is the first to present a unified, comprehensive, and up-to-date treatment of net theory. It brings together elements of abstract graph theory and circuit analysis to network problems. English. Machine theory. http://id.loc.gov/authorities/subjects/sh85079341 Nets (Mathematics) http://id.loc.gov/authorities/subjects/sh85091044 Flowgraphs. http://id.loc.gov/authorities/subjects/sh85049350 System analysis. http://id.loc.gov/authorities/subjects/sh85131733 Systems Analysis https://id.nlm.nih.gov/mesh/D013597 Réseaux (Mathématiques) Graphes de fluence. Analyse de systèmes. Théorie des automates. systems analysis. aat MATHEMATICS Infinity. bisacsh MATHEMATICS Logic. bisacsh System analysis fast Nets (Mathematics) fast Flowgraphs fast Machine theory fast Print version: Chen, Wai-Kai, 1936- Net theory and its applications. London : Imperial College Press, 2003 1860942261 9781860942266 (DLC) 2005281859 (OCoLC)52785429 Series in electrical and computer engineering ; vol. 1. http://id.loc.gov/authorities/names/no2003123710 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=235547 Volltext |
spellingShingle | Chen, Wai-Kai, 1936- Net theory and its applications : flows in networks / Series in electrical and computer engineering ; 1. Graphs and networks. 1.1. Basic definitions of abstract graphs. 1.2. Operations on graphs. 1.3. Nonseparable graphs and bipartite graphs. 1.4. Planar graphs. 1.5. Dual graphs. 1.6. 2-isomorphism. 1.7. Matrices associated with a graph. 1.8. Directed graphs. 1.9. The circuit matrix associated with a planar graph or directed graph. 1.10. Summary and suggested reading -- 2. The shortest directed path problem. 2.1. Shortest directed paths. 2.2. Shortest directed path algorithms. 2.3. Multiterminal shortest directed paths. 2.4. Enumeration of the shortest directed paths by decomposition. 2.5. Summary and suggested reading -- 3. Maximum flows in networks. 3.1. Flows. 3.2. s-t cuts. 3.3. Maximum flow. 3.4. Ford-Fulkerson algorithm. 3.5. Layered nets. 3.6. A blocking flow algorithm. 3.7. Variants of the Ford-Fulkerson algorithm. 3.8. Karzanov algorithm. 3.9. Flows in undirected and mixed nets. 3.10. Flows in node-and-arc capacitated nets. 3.11. Summary and suggested reading -- 4. Minimum trees and communication nets. 4.1. Forests, subtrees and trees. 4.2. Minimum and maximum trees. 4.3. Minimum and maximum tree algorithms. 4.4. Terminal capacity matrix. 4.5. Synthesis of a flow-equivalent tree. 4.6. Synthesis of optimum undirected communication nets. 4.7. Oriented communication nets. 4.8. Summary and suggested reading -- 5. Feasibility theorems and their applications. 5.1. A supply-demand theorem. 5.2. An extended supply-demand theorem. 5.3. Circulation theorem. 5.4. Feasible circulation algorithm. 5.5. Flows in nets with lower bounds on arcs. 5.6. Feasible flows in node-and-arc capacitated nets. 5.7. Summary and suggested reading -- 6. Applications of flow theorems to subgraph problems. 6.1. The subgraph problem of a directed graph. 6.2. Digraphic sequences. 6.3. The subgraph problem of a graph. 6.4. Graphical sequences. 6.5. The (p, s)-matrix. 6.6. Realization of the 1-matrix and the (1, 0)-matrix. 6.7. Minimal transformations. 6.8. Summary and suggested reading -- 7. Signal-flow graphs. 7.1. The signal-flow graph. 7.2. Topological evaluation of determinants. 7.3. Topological evaluation of cofactors. 7.4. Topological solutions of linear algebraic equations. 7.5. Equivalence and transformation. 7.6. The matrix inversion. 7.7. Signal-flow graph formulation of feedback amplifier theory. 7.8. Matrix signal-flow graph. 7.9. The multiple-loop feedback amplifier theory. 7.10. Summary and suggested reading -- 8. Other net applications. 8.1. Boolean matrices and switching nets. 8.2. Tellegen's theorem. 8.3. Generalized signal-flow graphs. 8.4. Permutations by spaghetti Amida. 8.5. The Amida graph. 8.6. Graph decomposition and hybrid analysis of electrical networks. 8.7. Summary and suggested reading. Machine theory. http://id.loc.gov/authorities/subjects/sh85079341 Nets (Mathematics) http://id.loc.gov/authorities/subjects/sh85091044 Flowgraphs. http://id.loc.gov/authorities/subjects/sh85049350 System analysis. http://id.loc.gov/authorities/subjects/sh85131733 Systems Analysis https://id.nlm.nih.gov/mesh/D013597 Réseaux (Mathématiques) Graphes de fluence. Analyse de systèmes. Théorie des automates. systems analysis. aat MATHEMATICS Infinity. bisacsh MATHEMATICS Logic. bisacsh System analysis fast Nets (Mathematics) fast Flowgraphs fast Machine theory fast |
subject_GND | http://id.loc.gov/authorities/subjects/sh85079341 http://id.loc.gov/authorities/subjects/sh85091044 http://id.loc.gov/authorities/subjects/sh85049350 http://id.loc.gov/authorities/subjects/sh85131733 https://id.nlm.nih.gov/mesh/D013597 |
title | Net theory and its applications : flows in networks / |
title_auth | Net theory and its applications : flows in networks / |
title_exact_search | Net theory and its applications : flows in networks / |
title_full | Net theory and its applications : flows in networks / Wai-Kai Chen. |
title_fullStr | Net theory and its applications : flows in networks / Wai-Kai Chen. |
title_full_unstemmed | Net theory and its applications : flows in networks / Wai-Kai Chen. |
title_short | Net theory and its applications : |
title_sort | net theory and its applications flows in networks |
title_sub | flows in networks / |
topic | Machine theory. http://id.loc.gov/authorities/subjects/sh85079341 Nets (Mathematics) http://id.loc.gov/authorities/subjects/sh85091044 Flowgraphs. http://id.loc.gov/authorities/subjects/sh85049350 System analysis. http://id.loc.gov/authorities/subjects/sh85131733 Systems Analysis https://id.nlm.nih.gov/mesh/D013597 Réseaux (Mathématiques) Graphes de fluence. Analyse de systèmes. Théorie des automates. systems analysis. aat MATHEMATICS Infinity. bisacsh MATHEMATICS Logic. bisacsh System analysis fast Nets (Mathematics) fast Flowgraphs fast Machine theory fast |
topic_facet | Machine theory. Nets (Mathematics) Flowgraphs. System analysis. Systems Analysis Réseaux (Mathématiques) Graphes de fluence. Analyse de systèmes. Théorie des automates. systems analysis. MATHEMATICS Infinity. MATHEMATICS Logic. System analysis Flowgraphs Machine theory |
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work_keys_str_mv | AT chenwaikai nettheoryanditsapplicationsflowsinnetworks |